Abstract
We formulate a version of the information paradox in de Sitter spacetime and show that it is solved by the emergence of entanglement islands in the context of the DS/dS correspondence; in particular, the entanglement entropy of a subregion obeys a time-dependent Page curve. Our construction works in general spacetime dimensions and keeps the graviton massless. We interpret the resulting behavior of the entanglement entropy using double holography. It suggests that the spatial distribution of microscopic degrees of freedom depends on descriptions, as in the case of a black hole. In the static (distant) description of de Sitter (black hole) spacetime, these degrees of freedom represent microstates associated with the Gibbons-Hawking (Bekenstein-Hawking) entropy and are localized toward the horizon. On the other hand, in a global (effective two-sided) description, which is obtained by the quantum analog of analytic continuation and is intrinsically semiclassical, they are distributed uniformly and in a unique semiclassical de Sitter (black hole) vacuum state.
Highlights
Using double holography in the DS/de Sitter (dS) framework, we find that the standard, time-dependent Page curve is obtained while preserving the masslessness of the graviton
We present an apparent paradox involving dS spacetime, which we will resolve later using De Sitter/de Sitter (DS/dS) double holography
We have formulated a version of the information paradox in dS spacetime and shown that it is solved by the emergence of entanglement islands in the context of double DS/dS holography
Summary
Recent development in AdS/CFT holography provides important new elements to our understanding of the geometrization of the entanglement structure of the boundary conformal field theory (CFT), called “entanglement islands” [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. We take the view that, to obtain the standard Page curve, we must focus on fine-grained entropy of semiclassical Hawking radiation in a weakly gravitating regime and not the fine-grained entropy of the full microscopic degrees of freedom We postulate that this can be done by fixing the boundary of the region on the second brane for which the entanglement entropy is calculated, rather than determining it by extremization.. Summarizing, quantum gravity in dSdþ is dual to two UV-cutoff CFTs living on dSd coupled to each other via dynamical gravity [57] In this context, questions regarding entanglement entropy, how the duality works, and its implications for the underlying fast scrambling dynamics have been studied in recent years, where several important progresses have been made [54,65,66,67,68,69,70].
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